Help with a problem about motion — bullet striking a block of wood

In summary, the particle will have a downward velocity and a horizontal velocity. It will travel a distance of 0.24 m/s after the collision.
  • #1
TextClick
7
0
Homework Statement
A bullet of mass 0.0020 kg traveling at 600.0 m/s embeds in a block of wood sitting on the edge of a cliff. The mass of the block is 5.0 kg and it lands 0.72 m from the base of the cliff. How tall is the cliff?
Relevant Equations
m1v1+m2v2=(m1+m2)vf
d=vit+1/2at^2
Fdeltat=mdeltav
F=ma
I first plugged my given values into m1v1+m2v2=(m1+m2)vf.

(0.002)(600)+(5)(0)=((0.0020)+(5))vf
vf=0.24 m/s

Next, I plugged my given values into F=ma.

((0.002)+(5))(9.8)
F=49.02 N

Next, I plugged my given values into Fdeltat=mdeltav.

deltat=mdeltav/F

((0.002)+(5))(0.24)/(49.02)
deltat=0.02448 s

Finally, I plugged my given values into y=vit+1/2at^2.

y=1/2(9.8)(0.02448)
y=0.12 m
 
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  • #2
TextClick said:
F=49.02 N

Next, I plugged my given values into Fdeltat=mdeltav.

deltat=mdeltav/F
The force you found is that due to gravity, so leads to a downward acceleration, and this occurs after the block is knocked off the top of the cliff.
The change in velocity you used there is horizontal, and occurs during the impact, before the block becomes airborne.
I see no basis for using them in the same equation.

Note you did not use the information about where the block lands. How can you use that to find the descent time?
 
  • #3
So I got the problem correct up to the point that I derived the initial velocity in the x direction, 0.24 m/s. After this point, I do not understand the methodology behind this problem.

The teacher told me to use the equation x=v1xt, plug in my given values, and solve for t to get 3 seconds.

The next step was to use the equation y=1/2gt, plug in my given values, and solve to get 14.7.

Can you please help me to understand this part? Thanks.
 
  • #4
TextClick said:
The teacher told me to use the equation x=v1xt, plug in my given values, and solve for t to get 3 seconds.
You found the horizontal velocity after impact. Thereafter there is no acceleration horizontally (we are ignoring drag). How far does it travel horizontally after the collision? How long will that take?
 
Last edited:
  • #5
TextClick said:
I first plugged my given values into m1v1+m2v2=(m1+m2)vf.

(0.002)(600)+(5)(0)=((0.0020)+(5))vf
vf=0.24 m/s

How will the trajectory of the particle look like? How many independent velocity components will it have at any given time mid fall?
 

1. What is the velocity of the bullet when it strikes the block of wood?

The velocity of the bullet can vary depending on factors such as the type of gun used, the distance between the gun and the block of wood, and any obstacles in the bullet's path. In order to accurately determine the velocity, a series of calculations and measurements would need to be taken.

2. How does the mass of the bullet affect its impact on the block of wood?

The mass of the bullet plays a significant role in its impact on the block of wood. A heavier bullet will have a greater force and momentum, resulting in a deeper penetration into the wood. On the other hand, a lighter bullet may not penetrate as deeply or have as much force upon impact.

3. Can the angle at which the bullet strikes the block of wood affect the outcome of the collision?

Yes, the angle at which the bullet strikes the block of wood can have a significant impact on the outcome of the collision. If the bullet strikes the wood at a perpendicular angle, it will likely have a deeper penetration and more force than if it were to hit at an angle.

4. How does the density of the wood affect the bullet's penetration?

The density of the wood can greatly affect the bullet's penetration. A denser wood, such as oak, will be harder for the bullet to penetrate compared to a softer wood, such as pine. The density of the wood also affects the amount of force and energy needed for the bullet to pass through it.

5. What is the significance of the bullet's shape in relation to its impact on the block of wood?

The shape of the bullet can greatly impact its penetration and force upon hitting the block of wood. For example, a pointed bullet will have a more focused impact and may penetrate deeper than a round bullet with a larger surface area. The shape of the bullet also affects its aerodynamics and trajectory, which can also impact the outcome of the collision.

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